Hatch will finish his sixth term in the Senate next year, giving him 36 years in the upper chamber.
Chaffetz, a Tea Party favorite and member of the conservative Republican Study Committee, also criticized Republicans in Congress who generally supported President Bush's No Child Left Behind law and the Troubled Asset Relief Program.
"They blew it," Chaffetz said.
Hatch's office responded by saying Hatch has a "lifetime conservative voting record of 90 percent after more than 12,000 votes." A spokeswoman for Hatch said Chaffetz has "spent the past week outside of his district dishonestly and inaccurately running down a fellow Republican."